Hi, OP -
Former STEM admission tutor here. I also taught in a Public Ivy for over 15 years so I can address some points others have not.
Firstly, as DS is not sure of his subject, Scotland might be his best bet. Y1 in Scotland, unlike the rest of the UK, is a generalist year. It is easier to switch between courses. Scottish degrees are four years for a Bachelors, five for M(Subject)
A Foundation Year if England is the destination as suggested by @ErrolTheDragon is also a good option, depending on how DS will react to the idea. Oxford and Imperial do not offer them. FY is meant to address gaps and I am not sure what these would be in the case of DS. However if British pedagogical style is substantially different to what he is used to, plunging into specialist Y1 at Oxford or Imperial could be a rather rude awakening.
You’ve mentioned at least by implication that DS has extracurriculars or other factors that carry weight in the US - as a Brit, you know they don’t matter here. Oxford wants evidence of (loathsome word) passion for subject. Has DS got that? Cannot be faked in interview with the experts who wrote the books.
Oxford requires the Physics Admissions Test (PAT) and Imperial the ESAT of all Engineering applicants. These are major screens for interview. I don’t think Edinburgh and St A’s use them but you can check
The Complete University Guide online will give subject matter rankings, Admissions requirements, etc. It is the best guide IMO
I usually agree with @titchy , I think it was, but the QS rankings are easily gameable. CUG rankings, the Times rankings and the Shanghai rankings are more reliable IMO. I like the Guardian rankings also, for the student perspective built in (not completely reliably).
You asked a good, granular question about teaching. The best answers will be found at the online forum The Student Room, for UK university students. There is also a similar reddit board. TSR is very good. DS should join these and post.
I understand what you are saying about his procrastination, but if it is so bad that he can’t do this relatively fun thing, perhaps he would benefit from a gap year - truthfully IMO many would. There is no UK university that looks out for students half as well as a good American one. We are very good at ticking the boxes, though, and that can give the same impression.
There UK consultants who work online with overseas clients. I will google this and see if any look familiar from when I was doing admissions. I will be back if there are. But the pandemic was hard on the sector so I expect it has changed a lot. I am not optimistic